Follow a worked example.
Every example below can be loaded using its calculator’s Reset example button. Inputs use centimetres, square centimetres or cubic centimetres as labelled, while angles use degrees.
Three sides (SSS)
Given: Side a = 3; Side b = 4; Side c = 5.
s = (a+b+c)/2; A = √[s(s−a)(s−b)(s−c)]
| Measurement | Calculated value |
|---|---|
| Area | 6 cm² |
| Perimeter | 12 cm |
| Altitude to side a | 4 cm |
| Angle opposite side a | 36.869898° |
Base and perpendicular height
Given: Base b = 8; Perpendicular height h = 5.
A = bh/2
| Measurement | Calculated value |
|---|---|
| Area | 20 cm² |
Two sides and included angle
Given: Side a = 5; Side b = 7; Included angle θ = 60.
c² = a²+b²−2ab cos θ; A = ab sin θ/2
| Measurement | Calculated value |
|---|---|
| Third side c | 6.244998 cm |
| Area | 15.155445 cm² |
| Perimeter | 18.244998 cm |
| Altitude to side a | 6.0621778 cm |
| Angle opposite side a | 43.897886° |
Third interior angle
Given: Angle α = 50; Angle β = 60.
γ = 180°−α−β
| Measurement | Calculated value |
|---|---|
| Third angle γ | 70° |
Check the answer’s dimensions
An area contains a product of two lengths, while volume contains three. A perimeter or radius is still a length. If your input measurements are mixed between metres and centimetres, convert them to a common unit first. A realistic-looking number can still be wrong if the units were inconsistent.